How to Make It
Prepare the Pickled Mushrooms: Bring water, rice vinegar, cider vinegar, soy sauce, salt, chiles, and star anise to a boil in a large pot over high. Add mushrooms, reduce heat to medium, and simmer until shiitake mushrooms have shrunk to 2/3 their original size, about 15 minutes. Remove from heat. Cool in liquid. Refrigerate overnight or up to 1 month.
Prepare the Au Jus: Bring stock, rice vinegar, soy sauce, salt, and white pepper to a boil in a small saucepot over high. Keep warm over low.
Heat 2 tablespoons of the oil in a large skillet over medium-high. Add tofu pieces; cook until lightly browned on both sides, 2 to 3 minutes per side. Transfer to a plate. Wipe skillet clean, and return to heat. Whisk together eggs, water, and salt. Add remaining 2 tablespoons oil to skillet. Add egg mixture. Cook, stirring once, until just set, about 90 seconds. Transfer to a plate.
To assemble sandwiches: Cut baguette crosswise but not all the way through, so you can unfold bread like a book. Hollow out baguette leaving a half-inch shell. Place 2 tofu slices in each baguette. Divide eggs and bamboo shoots between sandwiches. Add 1/2 cup mushrooms to each sandwich, and top with some of the watercress. Serve each with 1/2 cup hot Au Jus for dipping.